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pith:VKSV3N2Y

pith:2026:VKSV3N2Y2BNGISOI66PQKI7HG6

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Dean-Kawasaki Equation with Biot-Savart and Keller-Segel Interactions: Existence and Large Deviations

Xiaohao Ji, Yue Sun, Zhengyan Wu

The Dean-Kawasaki equation admits probabilistically weak renormalized kinetic solutions even with singular Biot-Savart and Keller-Segel interactions.

arxiv:2605.13479 v1 · 2026-05-13 · math.PR · math.AP

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Claims

C1strongest claim

We establish the existence of probabilistically weak, renormalized kinetic solutions to the Dean--Kawasaki equation with singular interaction kernels, including those of Biot--Savart and Keller--Segel type. Under a suitable regularization of the square-root noise coefficient, we further prove a restricted large deviation principle for probabilistically weak solutions to the regularized Dean--Kawasaki equation.

C2weakest assumption

A suitable regularization of the square-root noise coefficient exists that preserves the Dean-Kawasaki structure while allowing the exponential tightness argument and weak-strong uniqueness to close the large-deviation proof despite the scaling criticality of the singular kernels.

C3one line summary

Existence of probabilistically weak renormalized kinetic solutions and a restricted large deviation principle are established for the Dean-Kawasaki equation with Biot-Savart and Keller-Segel singular kernels via regularization and a new exponential tightness argument.

References

13 extracted · 13 resolved · 2 Pith anchors

[1] Variational representations for continuous time processes.Ann 2011 · doi:10.1214/10-aihp382

[2] [CD16] Jurandir Ceccon and Carlos E 2019 · doi:10.1016/j.crma.2019.09.007

[3] [Dea96] David S 1996 · doi:10.1002/9781118165904

[4] Conservative stochastic PDE and fluctuations of the sym- metric simple exclusion process.Communications in Mathematical Physics, 407:Paper No 2026 · doi:10.1214/20-ejp436

[5] [Due16] Mitia Duerinckx · doi:10.1007/s40072-024-00324-1

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First computed	2026-05-18T02:44:41.403102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaa55db758d05a6449c8f79f0523e7378b906662e8984b18e8f3676ae283fc98

Aliases

arxiv: 2605.13479 · arxiv_version: 2605.13479v1 · doi: 10.48550/arxiv.2605.13479 · pith_short_12: VKSV3N2Y2BNG · pith_short_16: VKSV3N2Y2BNGISOI · pith_short_8: VKSV3N2Y

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VKSV3N2Y2BNGISOI66PQKI7HG6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: aaa55db758d05a6449c8f79f0523e7378b906662e8984b18e8f3676ae283fc98

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "d50929f42dd805959520f77489296a0f2c1b44f3e9a18de7c6cf15d00bb8c9ff",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T13:05:51Z",
    "title_canon_sha256": "1c17e04b462dcf1ad1072a2eceb5ff86a3ff853bc0ee1fa58fe57a631d45f9d8"
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  "source": {
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    "kind": "arxiv",
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